Duct Fabricated with Additive Manufacturing and Having One or More Curves

ABSTRACT

Curvilinear ducts manufactured by depositing one or more runs of material in a conjoined helix, a conjoined plurality of conjoined planar spirals, and a plurality of conjoined conical spirals.

STATEMENT OF RELATED APPLICATIONS

The following patent applications are incorporated by reference fortheir description of how to make and use additive manufacturing system100:

-   -   U.S. patent application Ser. No. 15/375,832, filing date Dec.        12, 2016;    -   U.S. patent application Ser. No. 15/232,767, filing date Aug. 9,        2016;    -   U.S. patent application Ser. No. 14/574,237, filing date Dec.        17, 2014; and    -   U.S. patent application Ser. No. 14/623,471, filing date Feb.        16, 2015.

U.S. patent application Ser. No. 15/459,747 filed on Mar. 15, 2017,entitled “Duct Fabricated With Additive Manufacturing” is incorporatedby reference for its description of how to manufacture ducts usinghelices, planar spirals, and conical spirals. U.S. patent applicationSer. No. 15/459,630, filed on Mar. 15, 2017, is incorporated byreference herein.

FIELD OF THE INVENTION

The present invention relates to additive manufacturing, which is oftencolloquially called “3D Printing,” in general, and, more particularly,to manufacturing curvilinear ducts with additive manufacturing.

BACKGROUND

Additive manufacturing is a technique for building a three-dimensionalobject from a mathematical model of the object. In the additivemanufacturing technique called fused-deposition modeling, the object isbuilt by feeding a thermoplastic filament into a heated deposition head.The heated deposition head melts and deposits the molten thermoplasticmaterial as one or more runs of material. Typically, a run of materialis shaped like a thread or like the toothpaste that is squeezed from atube but much smaller. When a run is deposited, it is just slightlyabove its melting point. After it is deposited, the run quicklysolidifies and fuses with the runs that it touches.

Perhaps the greatest advantage of additive manufacturing is that it canbuild an object of any shape. To accomplish this, however, there areconstraints on the sequence in which the runs can be deposited. First,each run must be supported. In other words, a run cannot be deposited onair. Therefore, each run must be deposited on:

-   -   (i) a platform that is not part of the object, or    -   (ii) one or more previously-deposited runs that will be part of        the object, or    -   (iii) a temporary scaffold of support material that is not part        of the object, or    -   (iv) any combination of i, ii, and iii.        Second, when a three-dimensional surface is sealed, it is no        longer possible to deposit a run inside of that surface. This is        analogous to the situation in which once you close a box, you        can't put anything into the box.

There is a general methodology that is used in additive manufacturingthat satisfies these constraints and enables the building of an objectof any shape. The three-dimensional model of the object is modeled asthousands of thin horizontal layers. Each layer is modeled as thousandsof runs and voids. The object is then built, one run at a time, onelayer at a time, only in the ±X, ±Y, and +Z directions.

There are, however, costs and disadvantages associated with traditionaladditive manufacturing.

SUMMARY OF THE INVENTION

Embodiments of the present invention are able to fabricate curvilinearducts with additive manufacturing without some of the costs anddisadvantages for doing so in the prior art. For example, ductsfabricated in accordance with the illustrative embodiments have moreadvantageous mechanical properties in comparison to ducts fabricatedusing prior art techniques.

Furthermore, some of the ducts that are manufactured in accordance withthe illustrative embodiments comprise a continuous run of material,which enables advantageous mechanical properties in comparison to ductsthat are manufactured with a plurality of discontinuous runs ofmaterial.

The run of material in some embodiments of the present inventionchopped-fiber reinforced thermoplastic. It will be clear to thoseskilled in the art, after reading this disclosure, how to make and usealternative embodiments of the present invention in which the run ofmaterial is any satisfactory material.

A duct manufactured in accordance with the illustrative embodimentcomprises one or more segments, wherein each segment is straight orcurved. Furthermore, each segment is manufactured by depositing:

-   -   i. one or more conjoined helices, or    -   ii. one or more stacks of conjoined planar spirals, or    -   iii. one or more conjoined stacks of conical spirals, or    -   iv. any combination of i, ii, and iii.

Co-pending patent application entitled “Duct Fabricated With AdditiveManufacturing” (Attorney Docket 3019-130us 1) teaches how to make anduse straight segments of ducts from helices, stacks of planar spirals,and conical spirals. In order to make curved segments of ducts, however,the dimensions of these structures must be altered.

In particular, the duct axis {right arrow over (d)}(t) is a space curverepresented by the vector function:

{right arrow over (d)}(t)=

a(t),b(t),c(t)

and the longitudinal axis {right arrow over (r)}(s) of the run ofmaterial is a space curve described by the vector function:

{right arrow over (r)}(s)=

f(s),g(s),h(s)

The value of the value of the conjoining axis j(t) at {right arrow over(r)}(s) is proportional to the distance between {right arrow over(r)}(s) and the center of curvature {right arrow over (p)}(t):

j(t)>∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥

This enables the run of material to remain conjoined and form a curvedduct.

All dimensions and coordinates in this specification are stated inmillimeters in a right-hand Cartesian and/or cylindrical coordinatesystem. It will be clear to those skilled in the art how to convert fromone coordinate system to the other, and both coordinate systems will beused interchangeably. It will, however, be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention that use any (small “m”) metricsystem and any coordinate system.

It will be clear to those skilled in the art, after reading thisdisclosure, that the geometric descriptions of the illustrativeembodiments are ideals and that the imperfection of manufacturing mightproduce objects with inconsequential differences in dimensions andgeometry.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentof the present invention.

FIG. 2 depicts an illustration of an orthographic view of duct 151,which is an illustrative embodiment of the present invention.

FIG. 3 depicts an illustration of a cross-sectional view of duct 151.

DETAILED DESCRIPTION

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentof the present invention. Additive manufacturing system 100 comprises:CAD/CAM system 101, build chamber 102, turn-table 110, depositionplatform 111, robotic arm 121 (which itself comprises deposition head122 and deposition nozzle 123), thermoplastic filament spool 130, andthermoplastic filament 131. The purpose of manufacturing system 100 isto manufacture duct 151.

CAM controller 101 comprises the hardware and software necessary todirect build chamber 102, control robotic arm 121, deposition head 122,deposition nozzle 123, and turntable 110 to manufacture duct 151. Itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use CAM controller 101.

Build chamber 102 is a thermally-insulated, temperature-controlledenvironment in which duct 151 is manufactured. It will be clear to thoseskilled in art how to make and use build chamber 102.

Turn-table 110 comprises a stepper motor under the control of CAMcontroller 101 that is capable of rotating platform 111 (and,consequently duct 151) around the Z-axis. In particular, turn-table 110is capable of:

-   -   i. rotating platform 111 clockwise around the Z-axis from any        angle to any angle, and    -   ii. rotating platform 111 counter-clockwise around the Z-axis        from any angle to any angle, and    -   iii. rotating platform 111 at any rate, and    -   iv. maintaining (statically) the position of platform 111 at any        angle.        It will be clear to those skilled in the art how to make and use        turn-table 110.

Platform 111 comprises hardware on which duct 151 is manufactured.

It will be clear to those skilled in the art how to make and useplatform 111.

Robotic arm 121 is a seven-axis arm capable of placing deposition nozzle123 at any location in the build volume of duct 151 and from anyapproach angle. Furthermore, robotic arm can move deposition nozzle 123in:

-   -   i. the +X direction,    -   ii. the −X direction,    -   iii. the +Y direction,    -   iv. the −Y direction,    -   v. the +Z direction,    -   vi. the −Z direction, and    -   vii. any combination of i, ii, iii, iv, v, and vi        while rotating the approach angle of deposition nozzle 123        around any point or temporal series of points. It will be clear        to those skilled in the art how to make and use robotic arm 121.

Deposition head 122 is hardware that heats and deposits filament 131(which may partially or wholly contain one or more fiber strands) viadeposition nozzle 123.

Thermoplastic filament 131 comprises a continuous tow of carbon fiberthat is impregnated with a thermoplastic, but it will be clear to thoseskilled in the art, after reading this disclosure, how to make and usealternative embodiments of the present invention in which thermoplasticfilament 131 has a different fiber composition as described in U.S.patent application Ser. No. 14/184,010, which is incorporated byreference.

Thermoplastic filament 131 is deposited as a “run of material,” which isnot shown in FIG. 1 as distinct from duct 151. The physical andgeometric properties of the runs of material are described below and inthe accompanying figures.

FIG. 2 depicts an illustration of an orthographic elevation view of duct151 in accordance with the illustrative embodiment of the presentinvention.

Duct 151 is a curvilinear duct that is capable of directing the flow ofa fluid between opening 231 and 231. The curvature of duct 151 isdefined by a three-dimensional space curve called the duct axis {rightarrow over (d)}(t).

In order to facilitate an understanding of the present invention, theduct axis {right arrow over (d)}(t) of the illustrative embodiment isconfined to a plane. It will be clear to those skilled in the art, afterreading this disclosure, how to make and use alternative embodiments ofthe present invention in which duct axis {right arrow over (d)}(t) isnot confined to a plane (i.e., duct axis {right arrow over (d)}(t) is anon-linear and a non-planar space curve).

In accordance with the illustrative embodiment, duct axis {right arrowover (d)}(t) is described by a vector function whose general form is:

{right arrow over (d)}(t)=

a(t),b(t),c(t)

  (Eq. 1a)

where a(t), b(t), and c(t) are functions in a particular coordinatesystem (e.g., Cartesian, cylindrical, polar, etc.) and t is a realnumber in the domain t: [t₁, t₂]. It will be clear to those skilled inthe art how to describe any space curve, and, therefore, any duct axisas a vector function. Furthermore, it will be clear to those skilled inthe art how to represent the space curve of any duct axis usingmathematical techniques other than vector functions.

The particular vector function (in Cartesian coordinates) for duct axis{right arrow over (d)}(t) of duct 151 is:

$\begin{matrix}{{a(t)} = {\frac{800}{3}{\cos \left( \frac{\pi \; t}{500} \right)}}} & \left( {{{Eq}.\mspace{14mu} 1}b} \right) \\{{b(t)} = 0} & \left( {{{Eq}.\mspace{14mu} 1}c} \right) \\{{c(t)} = s} & \left( {{{Eq}.\mspace{14mu} 1}d} \right)\end{matrix}$

where t is a real number in the domain t: [0, 1000]. It will be clear tothose skilled in the art, after reading this disclosure, how todetermine the vector function for any duct axis in any coordinatesystem.

Duct axis {right arrow over (d)}(t) comprises curves, and the generalequation for the curvature κ(t) of duct axis {right arrow over (d)}(t)(expressed independently of any particular coordinate system) is:

$\begin{matrix}{{\kappa (t)} = {\frac{{{d(t)}^{\prime} \times {d(t)}^{''}}}{{{d(t)}^{\prime}}^{3}}.}} & \left( {{{Eq}.\mspace{14mu} 2}a} \right)\end{matrix}$

When the vector function of duct axis {right arrow over (d)}(t) isexpressed in Cartesian coordinates, the equation for the curvature κ(t)of is:

$\begin{matrix}{{\kappa (t)} = {\frac{\sqrt{\left( {{c^{''}b^{\prime}} - {c^{\prime}b^{''}}} \right)^{2} + \left( {{a^{''}c^{\prime}} - {a^{\prime}c^{''}}} \right)^{2} + \left( {{b^{''}a^{\prime}} - {a^{''}b^{\prime}}} \right)^{2}}}{\left( {a^{\prime 2} + b^{\prime 2} + c^{\prime 2}} \right)^{2/3}}.}} & \left( {{{Eq}.\mspace{14mu} 2}b} \right)\end{matrix}$

It will be clear to those skilled in the art how to compute thecurvature κ(t) of any duct axis for any value of the parameter t.

The radius of curvature δ(t) of duct axis {right arrow over (d)}(t)equals:

$\begin{matrix}{{\delta (t)} = \frac{1}{\kappa (t)}} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$

which equals the distance from the duct axis dc(t) to the center ofcurvature {right arrow over (p)}(t), which is a space curve that isdescribed by the vector function:

{right arrow over (p)}(t)=

α(t),β(t),γ(t)

  (Eq. 4).

where α(t), β(t), and γ(t) are functions in the same coordinate systemas that used for describing duct axis {right arrow over (d)}(t). It willbe clear to those skilled in the art how to determine the center ofcurvature {right arrow over (p)}(t) for any duct axis {right arrow over(d)}(t). For example, it is well known to those skilled in the art thatthe center of curvature {right arrow over (p)}(t) is the point that liesat the radius of curvature δ(t) from duct axis {right arrow over (d)}(t)(i.e., δ(t)=∥{right arrow over (d)}(t)−{right arrow over (p)}(t)∥) inthe direction of the unit principal normal vector of duct axis {rightarrow over (d)}(t) (into the curve). As space curve {right arrow over(p)}(t) is known as the evolute of {right arrow over (d)}(t). When ductaxis {right arrow over (d)}(t) is a planar curve, the evolute of {rightarrow over (d)}(t) is also a planar curve. In contrast, when duct axis{right arrow over (d)}(t) is a non-planar space curve, the evolute of{right arrow over (d)}(t) is also a non-planar space curve.

In accordance with the illustrative embodiment, duct 151 comprises acontinuous run of material whose longitudinal axis {right arrow over(r)}(s) is a space curve described by the vector function:

{right arrow over (r)}(s)=

f(s),g(s),h(s)

  (Eq. 5)

where f(s), g(s), and h(s) are functions in the same coordinate systemas that used for describing duct axis {right arrow over (d)}(t). It willbe clear to those skilled in the art, after reading this disclosure, howto determine the vector function for whose longitudinal axis {rightarrow over (r)}(s) for any duct, whether it comprises a helix, one ormore planar spirals, or one or more conical spirals.

For curved ducts and the curved portions of curvilinear ducts, the valueof the conjoining axis j(t) is a function of t. In particular, the valueof the conjoining axis j(t) at {right arrow over (r)}(s) is proportionalto the distance between {right arrow over (r)}(s) and the center ofcurvature {right arrow over (p)}(t):

j(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥  (Eq. 6).

This enables the run of material to remain conjoined and form a curvedduct. In accordance with the illustrative embodiment, the range of j(t)is between 0.1 millimeters and 0.5 millimeters, but it will be clear tothose skilled in the art, after reading this disclosure, how to selectthe values of j(t)—in accordance with Equation 6—for any duct.

The value of the isolating axis i(t) depends on the deposition processand the desired mechanical characteristics of duct 151. For example, thevalue of the isolating axis i(t) can be a constant:

i(t)=I  (Eq. 7a).

Alternatively, the value of the isolating axis i(t) can also vary as afunction of the distance from {right arrow over (r)}(s) to the center ofcurvature {right arrow over (p)}(t):

i(t)∝j(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥  (Eq.7b).

In any case, it will be clear to those skilled in the art, after readingthis disclosure, how to select the particular values of i(t)—inaccordance with equations 7a or 7b—for any duct.

It will be clear to those skilled in the art, after reading thisdisclosure, how to modify any duct taught in the co-pending patentapplication entitled “Duct Fabricated With Additive Manufacturing” (U.S.patent application Ser. No. 15/459,747) to have one or more curvedsegments. For example, any duct can be manufactured by depositing acontinuous run of material in the form of a conjoined helix—with anyprofile including, but not limited to circular andrectangular-with-rounded corners. FIG. 3 depicts a cross-sectional viewof duct 151 featuring a rectangular-with-rounded-corners profile.Additionally, any duct can be manufactured by depositing a conjoinedstack of conjoined planar spirals—with each planar spiral having anyprofile including, but not limited to circular andrectangular-with-rounded corners. And still furthermore, any duct can bemanufactured by depositing a conjoined stack of conical spirals—witheach conical spiral having any profile including, but not limited tocircular and rectangular-with-rounded corners.

It is to be understood that the above-described embodiments are merelyillustrative of the present invention and that many variations of theabove-described embodiments can be devised by those skilled in the artwithout departing from the scope of the invention. It is thereforeintended that such variations be included within the scope of thefollowing claims and their equivalents.

What is claimed is:
 1. A duct with a duct axis {right arrow over (d)}(t) described by the vector function: {right arrow over (d)}(t)=

a(t),b(t),c(t)

, the duct comprising: a run of material having a longitudinal axis {right arrow over (r)}(s) described by the vector function: {right arrow over (r)}(s)=

f(s),g(s),h(s)

that forms a helix around the duct axis {right arrow over (d)}(t); wherein the duct axis {right arrow over (d)}(t) is characterized by a curvature κ(t) and a center of curvature {right arrow over (p)}(t) described by the vector function: {right arrow over (p)}(t)=

α(t),β(t),γ(t)

; wherein the curvature κ(t)>0; wherein the run of material is characterized by a conjoining axis j(t) at {right arrow over (r)}(s) such that j(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥; and wherein t is a real number in the domain t: [t₁, t₂] and s is a real number in the domain s: [s₁, s₂].
 2. The duct of claim 1 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s) such that i(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥.
 3. The duct of claim 1 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s) that is constant.
 4. The duct of claim 1 wherein the evolute of {right arrow over (d)}(t) is a non-planar space curve over the interval [t₁, t₂].
 5. The duct of claim 1 wherein the helix is a circular helix.
 6. The duct of claim 1 wherein the range of j(t) is between 0.1 millimeters and 0.5 millimeters.
 7. The duct of claim 1 wherein the run of material is chopped-fiber reinforced thermoplastic.
 8. A duct with a duct axis {right arrow over (d)}(t) described by the vector function: {right arrow over (d)}(t)=

a(t),b(t),c(t)

, the duct comprising: a run of material having a longitudinal axis {right arrow over (r)}(s,k) described by the vector function: {right arrow over (r)}(s,k)=

f(s,k),g(s,k),h(s,k)

that forms a first stack of planar spirals, comprising a first planar spiral around the duct axis {right arrow over (d)}(t); wherein the duct axis {right arrow over (d)}(t) is characterized by a curvature κ(t) and a center of curvature {right arrow over (p)}(t) described by the vector function: {right arrow over (p)}(t)=

α(t),β(t),γ(t)

; wherein the curvature κ(t)>0; wherein the run of material is characterized by a conjoining axis j(t) at {right arrow over (r)}(s,k) such that j(t)∝∥{right arrow over (r)}(s,k)−{right arrow over (p)}(t)∥; and wherein t is a real number in the domain t: [t₁, t₂], s is a real number in the domain s: [s₁, s₂], and k is an integer.
 9. The duct of claim 8 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s,k) such that i(t)∝∥{right arrow over (r)}(s,k)−{right arrow over (p)}(t)∥.
 10. The duct of claim 8 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s,k) that is constant.
 11. The duct of claim 8 wherein the first planar spiral is a circular planar spiral.
 12. The duct of claim 8 wherein the first planar spiral is a rectangular-with-rounded-corners planar spiral.
 13. The duct of claim 8 wherein the first planar spiral is a conjoined planar spiral.
 14. The duct of claim 8 wherein the first stack of planar spirals further comprises a second planar spiral around the duct axis {right arrow over (d)}(t), wherein the first planar spiral and the second planar spiral are conjoined with each other. 15-20. (canceled)
 21. The duct of claim 8 wherein a second stack of planar spirals is further formed, wherein the first stack of planar spirals and the second stack of planar spirals are conjoined with each other.
 22. The duct of claim 8 wherein the range of j(t) is between 0.1 millimeters and 0.5 millimeters. 